Encryption systems are used to encode messages for transmissions over unsecured communications media, e.g., the Internet, phone lines, etc. In a rudimentary system, for example, each letter in the message is replaced by the preceding letter in the alphabet. Thus, the message "IBM" is encrypted as "HAL," while the message "THE LAZY FOX" is encrypted as "SGD KZYX EPW." Anyone receiving such a message can readily decrypt the original message if they are aware of, or guess, the mechanistic technique.
Among the more advance encryption systems are those where an encrypted message can only be decrypted by persons having a secret password, or key. In so-called cryptographic systems, the key represents a determined way of symbol transformation, whereas in mathematical translation systems, the key represents an adopted way of translation. A common disadvantage of either such systems lays in the use of private keys, which can be discovered by guessing or by systematic search.
Comparing different public coding systems, it has been found that public coding systems based on techniques described in paper N.G. de Bruijn, "A Combinatorial Problem," Proc. Netherlands' Acad. van Wtenschappen, vol. 49, pp: 758-764; 1946 are successful. These systems rely on the use of perfect maps, which may be defined as follows:
Given positive integers r, s, u, and v, a perfect map (r, s, u, v) is defined as a periodic binary array r x s in which binary subarray u x v occurs only once as a periodic subarray.
It is obvious that this definition is based on a field GF(2). Introducing two-dimensions, a shifting in two dimensions is enabled, therefore a given, two-dimensional binary array can be transformed in a protected sequence using a regular translation function. Hence, the discovering of a key used to make a protected sequence is hardened. A disadvantage of this method lays in the regularity of message protection, which can be discovered anyway, because it is not dependent on pervious messages. A subarray u x v repeats regularly, which is obvious from the linear recurrence: EQU (E.sup.m +.SIGMA.a.sub.j E.sup.m-i)S.sub.i -0
In view of the foregoing, an object of the invention is to provide improved systems for transmission of message and, more particularly, improved encryption of messages transferred over potentially unsecured media.